Effect of Double-Hyperconjugation on the Apparent Donor Ability of Σ-Bonds: Insights from the Relative Stability of Δ-Substituted Cyclohexyl Cations

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Effect of Double-Hyperconjugation on the Apparent Donor Ability of σ-Bonds: Insights from the Relative Stability of δ-Substituted Cyclohexyl Cations

Igor V. Alabugin* and Mariappan Manoharan Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390

[email protected]

Received September 27, 2004

A combination of electronic, structural, and energetic analyses shows that a somewhat larger intrinsic donor ability of the C-H bonds compared to that of C-C bonds can be overshadowed by cooperative hyperconjugative interactions with participation of remote substituents (double hyperconjugation or through-bond interaction). The importance of double hyperconjugation was investigated computationally using two independent criteria: (a) relative total energies and geometries of two conformers (“hyperconjomers”) of δ-substituted cyclohexyl cations (b) and natural bond orbital (NBO) analysis of electronic structure and orbital interactions in these molecules. Both criteria clearly show that the apparent donor ability of C-C bonds can vary over a wide range, and the relative order of donor ability of C-H and C-C bonds can be easily inverted depending on molecular connectivity and environment. In general, relative donor abilities of σ bonds can be changed by their through-bond communication with remote substituents and by greater polarizability of C-X bonds toward heavier elements. These computational results can be confirmed by experimental studies of conformational equilibrium of δ-substituted cyclohexyl cations.

Introduction the relative ability of many common σ donors, including the most ubiquitous case of C-HvsC-C bonds, is still Hyperconjugation, or delocalization which involves σ widely debated.4 An often discussed example involves bonds, manifests itself in numerous stereoelectronic stereoelectronic control in nucleophilic addition to cyclo- 1,2 effects controlling organic structure and reactivity. In hexanones and related compounds. A widely discussed particular, such interactions can deliver electron density model proposed by Cieplak suggests that the decisive to electron-deficient centers and, thus, are often sug- stereoelectronic factor determining axial approach of gested to determine stereoselectivity of organic reactions nucleophilic attack on the CdO group involves electron where the transition states for stereodivergent pathways donation from axial C-H bonds to the antibonding orbital are characterized by different relative arrangements of associated with the incipient (forming) bond between donor and acceptor orbitals. incoming nucleophile (Nu) and the carbonyl carbon. In - - It is well established that donors such as C Si, C Ge, this model, the axial approach is favored because the - and C Sn bonds are capable of providing significant above stabilizing interaction is more efficient than the 3 stabilization to a developing positive charge. However, analogous interaction with C-C-bonds during the equatorial approach of Nu (Figure 1).5 The larger donor ability (1) (a) Kirby, A. J. The Anomeric Effect and Related Stereoelectronic Effects at Oxygen; Springer-Verlag: Berlin, 1983. (b) The Anomeric Effect and Associated Stereoelectronic Effects; Thatcher, G. R. J., Ed.; (3) (a) Green, A. J.; Giordano, J.; White, J. M. Aust. J. Chem. 2000, ACS Symposium Series 539; American Chemical Society: Washington, 53, 285. For a review of interactions of C-MR3 bonds with acceptor DC, 1993. (c) Juaristi, E.; Guevas, G. The Anomeric Effect; CRC orbitals, with remote electron-deficient orbitals, π systems, etc., see: Press: Boca Raton, FL, 1994. (d) Juaristi, E., Ed. Conformational White, J. M.; Clark, C. I. Top. Stereochem. 1999, 22, 137. (b) Lambert, Behavior of Six-Membered Rings; VCH Publishers: New York, 1995. J. B.; Zhao, Y.; Emblidge, R. W.; Salvador, L. A.; Liu, X.; So, J.-H.; (e) For a recent experimental example and leading references, see Chelius, E. C. Acc. Chem. Res. 1999, 32, 183. Lambert, J. B.; Wang, also: Uehara, F.; Sato, M.; Kaneko, C.; Kurihara, H. J. Org. Chem. G. T.; Teramura, D. H. J. Org. Chem. 1988, 53, 5422. Lambert, J. B.; 1999, 64, 1436. Wang, G. T.; Finzel, R. B.; Teramura, D. H. J. Am. Chem. Soc. 1987, (2) Cohen, T.; Lin, M.-T. J. Am. Chem. Soc. 1984, 106, 1130. 109, 7838. Lambert, J. B. Tetrahedron 1990, 46, 2677. (c) Cook, Mi. Danishefsky, S. J.; Langer, M. Org. Chem. 1985, 50, 3672. Rychnovsky, A.; Eaborn, C.; Walton, D. R. M. J. Organomet. Chem. 1970, 24, 293. S. D.; Mickus D. E. Tetrahedron Lett. 1989, 30, 3011. Vedejs, E.; Dent, (4) For the most recent experimental study and an excellent historic W. H. J. Am. Chem. Soc. 1989, 111, 6861. Juaristi, E.; Cuevas, G.; survey of this problem, see: Spiniello, M.; White, J. M. Org. Biomol. Vela, A. J. Am. Chem. Soc. 1994, 116, 5796. Salzner, U.; Schleyer P. Chem. 2003, 1, 3094. v. R. J. Org. Chem. 1994, 59, 2138. Vedejs, E.; Dent, W. H.; Kendall, (5) (a) Cieplak, A. S. J. Am. Chem. Soc. 1981, 103, 4540. (b) Cieplak, J. T.; Oliver, P. A. J. Am. Chem. Soc. 1996, 118, 3556. Cuevas, G.; A. S.; Tait, B. D.; Johnson, C. R. J. Am. Chem. Soc, 1989, 111, 8447. Juaristi, E.; Vela, A. THEOCHEM 1997, 418, 231. Anderson, J. E.; For the Felkin-Ahn model of stereoselectivity of these reactions which Cai, J.; Davies, A. G. J. Chem. Soc., Perkin Trans. 2 1997, 2633. depends on acceptor ability of σ bonds, see: Cherest, M.; Felkin, H.; Wiberg, K. B.; Hammer, J. D.; Castejon, H.; Bailey, W. F.; DeLeon, E. Prudent, N. Tetrahedron Lett. 1968, 2199. Cherest, M.; Felkin, H. L.; Jarret, R. M. J. Org. Chem. 1999, 64, 2085. Juaristi, E.; Rosquete- Tetrahedron Lett. 1968, 2205. Cherest, M. Tetrahedron 1980, 36, 1593. Pina, G. A.; Vazquez-Hernandez, M.; Mota, A. J. Pure Appl. Chem. Ahn, N. T.; Eisenstein, O. Tetrahedron Lett. 1976, 155. Ahn, N. T. Top. 2003, 75, 589. Curr. Chem. 1980, 88, 145.

FIGURE 2. Axial and equatorial “hyperconjomers” of cyclohexyl cations.

greater donating ability of C-H bonds compared to that of C-C bonds. Although these results are consistent with the trends in 13C NMR chemical shifts of the â-carbon in â-substituted styrenes in solvents of different polarity,13 FIGURE 1. Most important transition-state-stabilizing hy- the opposite trend found in the gas-phase pyrolysis of perconjugative interactions for axial and equatorial nucleo- 1-arylethyl acetates cast a shadow of doubt at the original philic addition to cyclohexanone according to Cieplak’s model. interpretation of the Nathan-Baker effect.14 To compli- of C-H bonds compared to that of σ C-C bonds is the cate the matter even further, a recent study of two cornerstone of this model.6 This suggestion stimulated conformers of cyclohexyl cations with two distinctly many experimental7 and theoretical8 studies, some of different patterns of hyperconjugative interactions (“hy- which questioned the order of relative donor abilities of perconjomers”, Figure 2) found that a switch in the order - - σ C-C and C-H bonds. of the apparent donor ability of C H and C C bonds in The uncertainly of relative donor abilities of C-H and solution vs the gas phase occurs in the opposite direc- 15 C-C bonds is not surprising because the difference tion. Although the isomer stabilized preferentially by - f + between these two bonds is not large in ground-state σ(C H) n(C ) hyperconjugation is more stable accord- neutral molecules. For example, a careful low-tempera- ing to the gas-phase computations, the opposite order of ture X-ray structural study by Spinello and White found stability was observed in experimental studies in solution that the differences in donor ability of C-C and C-H and in computations including solvation effects (vide bonds toward σ(C-O) acceptors of variable electronic infra). demand are comparable to the experimental uncertainty Taking into account the fundamental importance of of measurements.4 Two recent computational studies also this question and conflicting literature results, we de- found that the differences are small. Natural bond orbital cided to determine the intrinsic order of donor ability of - - (NBO) analysis indicates that C-H bonds are slightly C H and C C σ bonds in systems where the differences better donors than σ C-C bonds in cyclohexane and in donor ability of σ bonds may be significantly large to related molecules.9 A similar conclusion was made by lead to experimentally observable consequences. Our Rablen and co-workers in a theoretical study on the origin choice of the model systems was inspired by the above 15 of gauche effects in substituted fluoroethanes.10 Note, elegant recent study of Rauk and co-workers who however, that the small differences in neutral molecules reported the dramatic effect of hyperconjugation on two 16 do not prevent these effects from becoming significant isomeric chair conformers of 1-Me-1-cyclohexyl cation in species with increased electron demand.11 differing in having the carbocation p-orbital oriented This importance has been well-recognized but also either “axially” or “equatorially”. These conformers have debated for quite a long time. For example, Nathan and distinctly different modes of hyperconjugative stabiliza- 15 Baker reported that a Me group provides more stabilization. The axial cationic orbital in the first hypercon- - tion to the developing positive charge at the p-benzylic jomer interacts strongly with the adjacent axial C H position than Et, i-Pr, and t-Bu groups in solvolysis of bonds whereas the equatorial vacant p-orbital in the p-alkyl-substituted benzyl bromides (Me > Et > i-Pr > second cation interacts most strongly with the anti- - t-Bu)12 and attributed this order of reactivity to the periplanar C C bonds (Figure 2). The contrasting nature of dominant hyperconjugative (6) For a detailed account of theoretical and experimental manifes- interactions in the two cyclohexyl cation conformers tations of differences in the C-HvsC-C hyperconjugation, see pp raises an intriguing question of whether the relative 1280-1282 in: Cieplak, A. S. Chem. Rev. 1999, 99, 1265. stability of these experimentally observable species can (7) From a special issue on diastereoselection: Mengel, A.; Reiser, O. Chem. Rev. 1999, 99, 1191. Dannenberg, J. J. Chem. Rev. 1999, 99, be taken as a measure of the relative donor ability of 1225. Gung, B. W. Chem. Rev. 1999, 99, 1377. Kaselj, M.; Chung, W.- C-H and C-C bonds toward a carbocationic center. If S.; Le Noble, W. J. Chem. Rev. 1999, 99, 1387. Adcock, W. Trout, N. this assumption is warranted, the greater stability of the A. Chem. Rev. 1999, 99, 1415. Wipf, P.; Jung, J.-K. Chem. Rev. 1999, 99, 1469. See also ref 6. “equatorial” conformer (ca. 0.6 kcal/mol according to (8) Tomoda, S. Chem. Rev. 1999, 99, 1243. Metha, G. Chan- B3LYP/6-31G*+ZPVE gas-phase calculations) could be drasekhar, J. Chem. Rev. 1999, 99, 1437. Ohwada, T. Chem. Rev. 1999, taken as evidence that C-C bonds are slightly better 99, 1337. (9) Alabugin I. V. J. Org. Chem. 2000, 65, 3910 and references therein. The same study also found that the order of donor ability of (12) Baker, J. W.; Nathan, W. S. J. Chem. Soc. 1935, 1844. σ C-X bonds in heterocyclohexanes is controlled by electronegativity (13) Cooney, B. T.; Happer, D. A. R. Aust. J. Chem. 1987, 40, 1537. of X and by stereoelectronic factors determined by molecular geometry. (14) Taylor, R.; Smith, G. G.; Wetzel, W. H. J. Am. Chem. Soc. 1962, (10) Rablen, P. R.; Hoffmann, R. W.; Hrovat, D. A.; Borden, W. T. 84, 4817. J. Chem. Soc., Perkin Trans. 2 1999, 1719. For a classic study on donor (15) (a) Rauk, A.; Sorensen, T. S.; Maerker, C.; Carneiro, J. W. d. ability of σ C-X bonds where X is the first row element from Li to F, M.; Sieber, S.; Schleyer, P. v. R. J. Am. Chem. Soc. 1996, 118, 3761. see: Apeilog, Y.; Schleyer, P. v. R.; Pople, J. A. J. Am. Chem. Soc. 1977, (b) Rauk, A.; Sorensen, T. S.; Schleyer, P. v. R. J. Chem. Soc., Perkin 99, 5901. Trans. 2 2001, 869. (11) For a discussion of the role of increased electron demand on (16) It was suggested originally that the “twist-boat” and “chair” weak hyperconjugative interactions for the case of homoanomeric conformers were in equilibrium but further studiesconfirmed the effects, see ref 26. existence of two isomeric chair cations.

9012 J. Org. Chem., Vol. 69, No. 26, 2004 Effect of Double-Hyperconjugation on the Donor Ability of σ-Bonds

a way to correlate computational analysis with potentially experimentally observable equilibrium changes in substituted cyclohexyl cations which are common inter- mediates in solvolysis reactions.20,21

Computational Details All cyclohexyl cation geometries were fully optimized at the FIGURE 3. δ-Substituted cyclohexyl cations: choice of sub- B3LYP/6-31G** and B3LYP/6-311++G** levels using the stituents and nature of orbital interactions. Gaussian 98 program.22 Electronic properties of model compounds were studied using the natural bond orbital (NBO) donors than C-H bonds. Unfortunately, the situation is 4.023 program implemented in Gaussian. Detailed descriptions far from being simple because the “axial” conformer is of the NBO calculations are available in the literature24 and experimentally ca. 1 kcal/mol more stable in solutions in the Supporting Information. the effect which is accurately reproduced by computations including solvation effects.15 Interestingly, the effect of Results and Discussion preferential solvation in this system is opposite to that 1. NBO Dissection of Hyperconjugative Contri- observed in the Nathan/Baker12 and Glyde/Taylor14 ex- butions to the Relative Stability of the Two Parent periments discussed above! The seeming discrepancy in Cyclohexyl Cations. To understand the nature of the estimates of the relative donor ability of C-H and delocalization effects involved in the two parent cyclo- C-C bonds in these cationic systems with theoretical hexyl cations, we carried out a detailed NBO analysis of predictions based on neutral molecules9,10 calls for a more the electronic structures of these species which is sum- detailed analysis of hyperconjugative interactions in marized in Figure 4. As suggested earlier by Rauk et al. these molecules which we will provide in the first part for 1-Me-cyclohexyl cations,15 we found that σ(C-C) f of this paper. n(C ) and σ(C-H) f n(C ) interactions play the domi- Another difference between the donor C-C and C-H 1 ax 1 - nant roles in stabilizing the equatorial and axial “hyper- orbitals is that, unlike â-C H bonds in the axial cation, conjomers”. Interestingly, the σ(C-C) f n(C ) interaction â,γ-C-C bonds in cyclohexyl cations are antiperiplanar 1 is larger than the σ(C-H)ax f n(C1) effect in contrast to not only to the equatorial cationic p-orbital but also to - f - ′ > - f - - the σ(C H)ax σ*(C H) ax σ(C H)eq σ*(C C) order an equatorial δ-C R bond (Figure 3). In the second part in neutral cyclohexane.9 This observation does not indi- of this paper, we analyze whether the presence of this cate inversion of the relative donor ability of C-H/C-C more extended hyperconjugative pattern is important in bondssits real origin lies a nonperfect overlap of the determining the apparent order of donor ability of C-C - - vacant orbital with the “axial” C2 H bond as a result of and C H bonds. We will focus on whether the “second planarization at C1. On the other hand, planarization sphere” hyperconjugative interactions with the remote donor δ-C-R orbitals are capable of positive charge (20) (a) Kirchen, R. P.; Sorensen, T. S. J. Am. Chem. Soc. 1978, 100, stabilization via through-bond communication with the 1487. (b) Kirchen, R. P.; Rankanayakulu, K.; Sorensen, T. S. J. Am. vacant p-orbitalsan effect also known as “double hyper- Chem. Soc. 1987, 109, 7811. (c) Finne, E. S.; Gunn, J. R.; Sorensen, T. conjugation”.17,18 We will investigate to what extent S. J. Am. Chem. Soc. 1987, 109, 7816. (d) Siehl, H.-U.; Vrcˇek, V.; Kronja, O. J. Chem. Soc., Perkin Trans. 2 2002, 106. double hyperconjugation is translated into electronic and (21) Facial selectivity in addition to rigid cyclic cations: Cheung, structural changes and whether this effect is capable of C. K.; Tseng, L. T.; Lin, M. H.; Srivastava, S.; le Noble, W. J. J. Am. changing the apparent order of C-H and C-C donor Chem. Soc. 1986, 108, 1598. Cheung, C. K.; Tseng, L. T.; Lin, M. H.; Srivastava, S.; le Noble, W. J. J. Am. Chem. Soc. 1987, 109, 7239. ability and whether these effects should be experimen- Srivastava, S.; le Noble, W. J. J. Am. Chem. Soc. 1987, 109, 5874. tally observable as different relative stabilities of “equa- Adcock, W.; Cotton, J.; Trout, N. A. J. Org. Chem. 1994, 59, 1867. Herrmann, R. Kirmse, W. Liebigs Ann. Chem. 1995, 699. Adcock, W.; torial” cations. Head, N. J.; Lokan, N. R.; Trout, N. A. J. Org. Chem. 1997, 62, 6177. In this analysis, we employ two complementary Filippi, A.; Trout, N. A.; Brunelle, P.; Adcock, W.; Sorensen, T. S.; criteriaseffects of δ-substituents at the relative energies Speranza, M.; J. Am. Chem. Soc. 2001, 123, 6396. Filippi, A. Chem. Eur. J. 2003, 9, 5396. Filippi, A.; Trout, N. A.; Brunelle, P.; Adcock, and structures of cyclohexyl cations (vide infra) and W.; Sorensen, T. S.; Speranza, M. J. Org. Chem. 2004, 69, 5537. dissection of orbital interactions using natural bond (22) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; orbital (NBO) analysis.19 This combination will provide Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; (17) Grob, C. A.; Rich, R. Tetrahedron 1978,29, 663. Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, (18) Lambert, J. B.; Ciro, C. M. J. Org. Chem. 1996, 61, 1940. C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; (19) For an illustrative rather than an exhaustive list of recent Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; applications of NBO method for analysis of chemical bonding, see: Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Reed, A. E.; Weinhold, F. Isr. J. Chem. 1991, 31, 277. Goodman, L.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Pophristic, V. T. Nature 2001, 411, 565. Salzner, U.; Schleyer P. v. R. Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; J. Org. Chem. 1994, 59, 2138. Gleiter, R.; Lange, H.; Borzyk, O. J. Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, Am. Chem. Soc. 1996, 118, 4889. Klod, S.; Koch, A.; Kleinpeter, E. J. W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Chem. Soc., Perkin Trans. 2 2002, 1506. Wilkens, S. J.; Westler, W. Pople, J. A. Gaussian 98, revision A.9; Gaussian, Inc.: Pittsburgh, PA, M.; Weinhold, F.; Markley, J. L. J. Am. Chem. Soc. 2002, 124, 1190. 1998. van der Veken, B. J.; Herrebout, W. A.; Szostak, R.; Shchepkin, D. N.; (23) NBO 4.0. Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Havlas, Z.; Hobza, P. J. Am. Chem. Soc. 2001, 123, 12290. Cortes, F.; Carpenter, J. E.; Weinhold, F. Theoretical Chemistry Institute, Tenorio, J.; Collera, O.; Cuevas, G. J. Org. Chem. 2001, 66, 2918. University of Wisconsin, Madison, WI, 1996. Uddin, J.; Boehme, C.; Frenking, G. Organometallics 2000, 19, 571. (24) Reed, A. E.; Weinhold, F. J. Chem. Phys. 1985,83, 1736. Gilbert, T. M. Organometallics 2000, 19, 1160. Xie, Y.; Grev, R. S.; Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988,88, 899. Gu, J.; Schaefer, H. F., III; Schleyer, P. v. R.; Su, J.; Li, X.-W.; Robinson, Weinhold F. In Encyclopedia of Computational Chemistry; Schleyer, G. H. J. Am. Chem. Soc. 1998, 120, 3773. Paddon-Row, M. N.; P. v. R., Ed. Wiley: New York, 1998; Vol. 3, p 1792. (b) See also: Shephard, M. J. J. Am. Chem. Soc. 1997, 119, 5355. www.chem.wisc.edu/∼nbo5.

J. Org. Chem, Vol. 69, No. 26, 2004 9013 Alabugin and Manoharan

FIGURE 4. Second-order perturbation NBO energies in kcal/mol for important hyperconjugative interactions in axial and equatorial cyclohexyl cations (B3LYP/6-31G**). also increases the overlap of the positive center with the cation (4.3 vs 3.7 kcal/mol) and neutral cyclohexanes (3.1 “equatorial” C2-H bond, thus allowing the cation to kcal/mol, R ) H; 3.2 kcal/mol, R ) Feq). In fact, one can benefit from the hyperconjugative interaction with two argue that such an increase in σ(C4-H)eq f σ*(C3-C2) donors at the same time. Although the energy of com- interaction in the parent system (which is estimated as bined σ(C-H)ax f n(C1) and σ(C-H)eq f n(C1) interac- ca. (2[4.3 - 3.7]) ) 1.2 kcal/mol provides a noticeable part tions in the “axial” conformer is greater than that of σ(C- of the larger stability of the equatorial cyclohexyl cation C) f n(C1) interactions in the “equatorial conformer (31.5 (1.9 kcal/mol) relative to that of the axial conformer. This vs 27.2 kcal mol-1), the balance of hyperconjugative observation provides evidence for extended charge delo- effects is tipped in favor of the “equatorial” conformer by calization through double hyperconjugation mecha- subtle effects involving remote donor moieties: γ-σ(C- nism.17,29,30 It also suggests that if stability of the H)eq f n(C1) homohyperconjugation with through space equatorial vs the axial cation is taken as a measure of participation of γ-C-H bonds25-27 and an increase in the the apparent donor ability of σ bridge C-C bonds toward δ-σ(C-H)eq f σ*(C-C) interaction which can be taken the acceptor p-orbital at the cationic center, in systems as a manifestation of double hyperconjugation (orbital shown in Figure 3, this stability should depend on the interaction through a bridge bond, vide infra).28 nature of equatorial substituent at the δ-position of Even though the close correspondence of the relative cyclohexyl cation. It also implies that, at least in some energies of combined hyperconjugative interactions in cases, apparently greater donor ability of C-C bonds can Figure 4 with the ca. 2 kcal mol-1 total energy differences be a result of higher order hyperconjugative interactions between two cations may be fortuitious (numerical with remote orbitals. Although, somewhat ironically, in results of the NBO perturbative analysis for strongly the case of the two hyperconjomers of unsubstituted delocalized systems should be taken with caution), this cyclohexyl cation this remote donor is a C-H bond, one picture is qualitatively correct in illustrating the rather can envision that other substituents may have a similar complex interplay of different hyperconjugative interac- or even larger effect. If this assumption is correct, tions. Importantly, this complexity precludes simply modulation of apparent donor ability of C-C bonds taking the difference between the two “axial” and “equa- should be even more important in the case of stronger torial” cyclohexyl cations as a direct measure of relative σ-donor δ-substituents. We will analyze these effects on donor abilities of C-H and C-C bonds. geometries, electronic structure, and energies in the On the other hand, the δ-σ(C-H)eq f σ*(C-C) interac- following sections. tion in the equatorial cation is noticeably increased in 2. δ-Substituted Cyclohexyl Cations. A. Substitu- comparison to the analogous interaction in the axial ent Effects at the Positive Charge Stabilization in Axial and Equatorial Cyclohexyl Cations. In this (25) Homohyperconjugation usually involves direct through space section, we will investigate the extent to which the interaction of the acceptor with the back lobe of the donor orbital. presence of δ-substituents affects energies of cyclohexyl Hoffmann, R.; Imamura, A.; Hehre, W. J. J. Am. Chem. Soc. 1968,90, 1499. cations. If only the “first sphere” effects or differences in (26) For a recent detailed discussion of homoanomeric effects, see: the intrinsic donor ability of C-H and C-C bonds are Alabugin I. V.; Manoharan, M.; Zeidan, T. A. J. Am. Chem. Soc. 2003, important, one would expect the relative energies of axial 125, 14014. (27) Homoconjugation is well established in chemistry of carboca- and equatorial “hyperconjomers” to be independent of the tions. Winstein, S.; Adams, R. J. Am. Chem. Soc. 1948, 70, 838. Sunko, δ-equatorial substituent R and only reflect the intrinsic D. E.; Hirsl-Starcevic, S.; Pollack, S. K.; Hehre, W. J. J. Am. Chem. - f - f Soc. 1979, 101, 6163 and references therein and all vast literature on difference between σ(C H) n(C) and σ(C C) n(C) nonclassical carbocations. interactions. On the other hand, if the “second sphere” (28) This phenomenon is important for C-Si and C-Sn bonds and has been called the δ effect: (a) Lambert, J. B.; Salvador, L. A.; So, (29) This is consistent with the unexpectedly large D isotope effects J.-H. Organometallics 1993, 12, 697. (b) Adcock, W.; Coope, J.; Shiner, in solvolysis in a topologically similar bicyclo[2.2.2]octane system V. J., Jr.; Trout, N. A. J. Org. Chem. 1990, 55, 1411. (c) Adcock, W.; reported by Adcock and co-workers in ref 28c. Kristic, A. R.; Duggan, P. J.; Shiner, V. J., Jr.; Coope, J.; Ensinger, M. (30) For effects of Si and Sn in additions of nucleophiles to W. J. Am. Chem. Soc. 1990, 112, 3140. (d) Lambert, J. B.; Salvador, adamantyl systems, see: Adcock, W.; Cotton, J.; Trout, N. A. J. Org. L. A. Tetrahedron Lett. 1990, 31, 3841. (e) Green, A. J.; Van, V.; White, Chem. 1994, 59, 1867. Adcock, W.; Head, N. J.; Lokan, N. R.; Trout, J. M. Austr. J. Chem. 1998, 51, 555. N. A. J. Org. Chem. 1997, 62, 6177.

9014 J. Org. Chem., Vol. 69, No. 26, 2004 Effect of Double-Hyperconjugation on the Donor Ability of σ-Bonds

FIGURE 5. Three isodesmic equations used to calculate substituent stabilization energies (SEs) in the equatorial and axial cyclohexyl cations.

TABLE 1. Substituent Stabilization Energies (SEs) in interplay of many factors such as hybridization26 and the Equatorial (SEeq) and Axial (SEax) Cyclohexyl inductive and field effects, which are still present in these Cations (kcal/mol) and Difference between Them species even when double hyperconjugation is minimized. (∆SEeq-ax ) SEeq - Seax) Computed at the B3LYP/6-31G** and B3LYP/6-311+G** Levels (Negative Values Indicate Interestingly, most of the δ-substituents are destabilizing Stabilization Relative to the Parent Cation) when compared to the unsubstituted “axial” cation (even such donors as Si, As, Ge).31 In the case of the two strongest σ donors (AlH2 and GaH2), the axial cations transform into more stable equatorial cations “in silico”, upon geometry optimization. In sharp contrast with the situation in “axial” cations, many substituents have a stabilizing effect on the “equatorial” cations (eq 2). Such effects can be rather large, indicating that δ-C-X bonds are capable of efficient interaction with the cation p-orbital as long as all orbitals participating in the double hyperconjugation interaction relay overlap efficiently. For the same reason, the destabilizing effects of σ acceptors such as C-halogen bonds are also more pronounced in equatorial cations. Thus, the above “equatorial” stabilization energies (SEeq) include stabilization or destabilization provided by σ C-X donors through the double hyperconjugation mechanism. They also include a number of other effects including those mentioned in the previous paragraph. Subtraction of axial (SEax) from equatorial (SEeq) stabilization energies provides the last isodesmic equa- tion of Figure 5 where the contributions of the above nonhyperconjugative (inductive, field, etc.) effects are partially compensated. Although this compensation is not perfect, the ∆SEeq-ax values give an improved estimate of the hyperconjugative stabilization of “equatorial” cations which has its source in the increase in double- hyperconjugative stabilization. Although none of three types of stabilization energies isolates hyperconjugative donation in its pure form, these energies are directly derived from experimentally obtain- able measurements and are defined in a way which a B3LYP/6-31G** level. b B3LYP/6-311++G** level. c The axial makes them important from a practical point of view. In conformers were transformed into their equatorial isomers upon the later sections of the paper, we will analyze relative geometry optimization. trends for these energies for elements of groups III-VII of the first three rows and compare these energies with hyperconjugation is relevant, substituent effects on sta- quantum-mechanical estimates of hyperconjugative do- bility of the axial and equatorial cations should be nor ability of σ bonds. noticeable. Although all of the above stabilization energies cor- These effects are estimated by the three isodesmic relate with the electronegativity of the respective sub- reactions given in Figure 5. The stabilization energies provided by these isodesmic reactions give different (31) The only notable exclusions are the cases of the strongest σ donorssAlH2 and GaH2 groups where axial cations are transformed information (Table 1). Effects of substituents in axial during the geometry optimization in the respective equatorial isomers cations which are described by eq 1 include a complicated stabilized by double hyperconjugation.

J. Org. Chem, Vol. 69, No. 26, 2004 9015 Alabugin and Manoharan

FIGURE 6. Correlations of substituent stabilization energies (SEs) in the “equatorial” (SEeq, left) and “axial” (SEax, right) cyclohexyl cations [B3LYP/6-31G**(B3LYP/6-311++G**)] with electronegativity of substituents R. Individual correlations for each period are shown in dashed lines.

FIGURE 7. Two correlations between the differences in stabilization energies of δ-XHn substituents in the equatorial and axial cyclohexyl cations (Figure 5) and electronegativity of the X. The top plot (a) corresponds to the general correlation; the bottom plot (b) gives separate correlations for each row. Calculations were performed at the B3LYP/6-31G** (B3LYP/6-311++G**) level (see Figure S2 in the Supporting Information for the correlation involving other electronegativity scales). stituents, especially for the second and third rows (see is increased in the “equatorial” cations where cationic the Supporting Information), Figure 6 reflects the ab- orbitals communicate better with the σ(C-R) bonds. sence of a general correlation for SEax values for elements Although the ∆SEeq-ax values from all periods are from different rows. The combined correlation for SEeq reasonably well described by a single correlation (Figure values is better but still noticeably scattered as a result 7) suggesting that the ∆SEeq-ax values indeed provide a of a rather complex interplay of different factors contrib- better estimate of the relative trends in hyperconjugative uting to the effects of substituents.32,33 Not surprisingly, donor ability of C-R bonds,36 the δ-substituents cluster sensitivity of stabilization energies to electronegativity into three groups. As shown in Figure 7a, the first group displays positive ∆SEeq-ax values and consists of cation- (32) In general, nonmetals from the second and third rows are destabilizing strongly electronegative acceptors with weaker “net” donors than one would expect from their electronegativity. Pauling electronegativity of g3. The second group in- On the other hand, the correlation slopes in Figure 6 become steeper for the heavier elements indicating that more polarizable C-R bonds cludes elements of intermediate electronegativity (ca. 2.5) are more sensitive to introduction of a positive charge. Stabilization which form C-R bonds with donor abilities close to that energies for the first period are not only significantly less sensitive to of C-H bonds (CH , SH, and SeH). The final group (R ) the electronegativity but also more scattered compared to the case of 3 SEs for the heavier elements which show almost perfect linear BH2,PH2, AsH2, SiH3, GeH3) includes relatively electro- correlations with electronegativity. The strongest deviation is observed positive substituents with negative ∆SEeq-ax values. In for the δ-BH substituent and can be attributed to the p-acceptor 2 this group, the ∆SE - values are scattered and elec- properties of boron atom. Due to the presence of the empty p-orbital eq ax on boron, the BH2 moiety provides very little stabilization to the tronegativity is not a good indicator of donor ability equatorial cation and slightly destabilizes the axial cation. (33) The observation that SEeq and SEax follow slightly different (34) The relative trend for H, Si and Ge are qualitatively consistent trends in different periods (see the Supporting Information) is not with the relative values of kinetic δ-effect for H/Si/Ge of 1.0/104/105.28 surprisingsits origin can be traced back to the trends in acceptor ability (35) For a recent analysis of the competition between anchimeric of σ bonds. In C-X σ bonds, this ability increases when going to the assistance and hyperconjugation in the interaction of a carbocationic end of a period and down a group. Enhancement of acceptor ability of center with S-, Se-, and Te-containing moieties, see: White, J. M.; C-X σ bonds as one moves from left to right in periods parallels the Lambert, J. B.; Spiniello, M.; Jones, S. A.; Gable, R. W. Chem. Eur. J. increase in electronegativity of X, whereas augmentation of acceptor 2002, 8, 2799. The results were consistent with the presence of strong ability in groups is opposite to the changes in electronegativity of X donation from the C-S and C-Se bonds without angular distortion. and in the C-X bond polarization, following instead the decrease in (36) Although the correlation coefficient is moderate, the R2 value the energy of σ*C-X orbitals. Alabugin I. V.; Zeidan, T. A. J. Am. for the correlation increases to 0.92 when the most deviating H and Chem. Soc. 2002, 124, 3175. BH2 groups are excluded. 9016 J. Org. Chem., Vol. 69, No. 26, 2004 Effect of Double-Hyperconjugation on the Donor Ability of σ-Bonds toward the δ-cationic center. The scattering may be partially due to a nonperfect compensation of the nonhyperconjugative effects but also is related to the differences in polarizabilities of C-R bonds in different periods as shown in Figure 7b.37 The divergence of the curves for different periods is caused by the fact that the more polarizable C-R bonds with heavier elements are more sensitive to the introduction of a positive charge at the remote position even when electronegativities of the respective elements is close (note H vs B and B vs Ge). The differences in polarizability between the elements of the first and second rows are especially pronounced. B. Effect on Geometries. In this section, we discuss the effect which double hyperconjugation imposes on the - - geometries of substituted cyclohexyl cations. In general, FIGURE 8. Correlation of the average C2 C3/C5 C6 bond lengths with electronegativity of substituents in the equatorial both of the two parent cation conformers are distorted cyclohexyl cations at the B3LYP/6-31G** (B3LYP/6-311++G**) from the ideal chair geometry and considerable changes level. in certain bond lengths are observed relative to the respective neutral molecules. These changes reflect de- correlations given in Figure 9 already provided a hint at localizing interactions needed to stabilize the positive the close connection between structures, energies, and charge. In the equatorial cation, the vacant p-orbital is electronic structures of δ-substituted cyclohexyl cations. tilted inside the ring with the simultaneous ring pucker- In the following sections, we will use NBO analysis to ing. In the axial cation, the cationic carbon is almost gain a better understanding of electronic effects respon- planarsthe C2-C1(+)-H-C6 torsion angle is ca. 175° sible for the observed trends in substituted cations. We whereas in the equatorial cations this torsion angle is will begin this discussion with a brief analysis of hyper- close to 165°.38 Direct hyperconjugation weakens and conjugation in equatorially substituted neutral cyclohex- lengthens the C2-C3 and C5-C6 bonds (ca. 1.613-1.686 anes. In general, presence of σ(C-C) f σ*(C-R) inter- Å) parallel to the vacant p-orbital in the equatorial cation action decreases population of the bridge σ(C-C) NBOs and the C2-Hax and C5-Hax bonds (ca. 1.120-1.22 Å) from the ideal population of 2.0 electrons. In a similar in the axial cation (Table S7, Supporting Information). way, σ(C-R) f σ*(C-C) interaction increases the popu- The bridge C-C bond is ca. 0.1 Å shorter in the respective lation of σ*(C-C) orbitals which are empty in the axial cations again illustrating the difference in the two idealized Lewis approximation. Figure 10 clearly shows major delocalizing modes (C-CvsC-H hyperconjuga- that population of bridge σ(C-C) bonds in neutral tions).39 These structural changes are similar to those cyclohexanes correlates with σ(C-C) f σ*(C-R) hyper- reported by Hrovat and Borden in an earlier theoretical conjugative interactions. As R becomes a stronger accep- study of substituent effects in 4-substituted bicycle[2.2.2]- tor, population of σ(C-C) orbitals decreases due to partial oct-1-yl cations.40 transfer of electron density to the acceptor σ*(C-R) When donor δ-substituents are introduced in the orbitals. Increased acceptor ability of σ C-R bonds from equatorial cation, the bridge C-C bond bond elongates. second and third rows is due to the lowering of the Introduction of σ-acceptors has an opposite effect (Table respective σ*(C-R) energies.33 S7 (Supporting Information), Figure 8). These structural When the positive charge is introduced, the slope of changes are closely associated with electronic properties the correlation of σ(C-C) population with electronega- and energies of equatorial cations as illustrated by Figure tivity of substituents changes its direction (Figure 11). 9, which shows that the length of the bridge C-C bonds This change indicates reversal in the direction of prevail- correlates well with the population of σ(C-C) bridge ing hyperconjugative effect. In other words, influence of orbitals (Figure 9a) and with the relative stabilities δ-C-R bonds is dominated by their acceptor ability in (Figure 9b) of equatorial and axial cations. In contrast, neutral cyclohexanes and by their donor ability in the the C-Heq bond length in the axial cations is nearly respective cations. This change is consistent with the independent of the nature of the remote substituents dramatically increased role of σ(C-R) f σ*(C-C) inter- (Table S7, Supporting Information). action. This interaction is coupled with the strong σ(C- C. NBO Analysis of Electronic Structure. (a) C) f n(C) hyperconjugation providing a mechanism for Substituent Effects on Distribution of Electron positive charge delocalization in these saturated mol- Density in δ-Substituted Cyclohexyl Cations. The ecules. The partial transfer of electron density from the donor orbitals to the vacant p-orbital of the cationic (37) For a discussion of the role of polarizibility of in donor ability, carbon atom through this mechanism is readily traced see: Taft, R. W.; Topsom, R. D. Prog. Phys. Org. Chem. 1987, 16,1. in the changes in electronic population of the donor and Exner, O.; Bo¨hm, S. J. Chem. Soc. 1997, 1235. (38) See the Supporting Information for the complete geometries of the acceptor orbitals. Whereas orbital populations in the all calculated species. axial cations are insensitive to the presence of a δ-sub- - (39) For the same reason, elongation of the “equatorial” C H bonds stituent (σ(C-H)ax, 1.849-1.862 e; nC1, 0.403-0.431 e; in the axial cations is smaller than that of the “axial” bonds even Table 3), populations of σ(C2-C3) (1.805-1.846 e) and though the σ(C-H)ax f n(C+) interaction also provides some stabilization to the axial cation. especially of nC1 (0.406-0.578 e) in the equatorial cations (40) Hrovat, D. A.; Borden, W. T. J. Org. Chem. 1992, 57, 2519. This show considerable variations (Table 3). These effects study showed the importance of electron correlation in describing double hyperconjugation and proved the deficiency of simple RHF clearly result from orbital interactions rather than from treatment of such systems. field effects because the respective changes in the popu-

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FIGURE 9. Correlations of the average C2-C3/C5-C6 bond lengths with (a) the average population of the corresponding σ- (C-C) orbitals and with (b) the relative energies of equatorial and axial cyclohexyl cations calculated at the B3LYP/6-31G** (B3LYP/6-311++G**) level. p-orbital, and thus, their population does not deviate considerably from the 2.0 e population of a perfectly localized σ bond (Tables 2 and 3). In contrast, populations of the remote σ(C-R) orbitals (Table 2, Figure 11) in equatorial cations are considerably reduced compared to the respective neutral molecules. Interestingly, the population of the δ-C-Heq orbital (1.946 e) is smaller than the population of the â-C-Hax orbital (1.965 e). Changes in the C-C and C-R bonds sum- marized in Figure 11 show that population of the bridge C-C bonds varies within 1.81-1.85 e whereas the population of C-R bonds spans the range of 1.786-1.989 e. Clearly, the C-R bonds undergo more dramatic changes despite being more distant from the vacant p-orbital. Together these observations illustrate again that in these systems spatial proximity and field effects are less important than correct orbital alignment (Table 2). FIGURE 10. Correlations of the population of donor σ(C-C) Another interesting observation is that the population orbitals with electronegativity of substituents from three of C-C bonds in equatorial cyclohexyl cations linearly different rows in equatorially substituted cyclohexanes at the ++ responds to electronegativity of R whereas such correla- B3LYP/6-31G**(B3LYP/6-311 G**) level (see Figure S3 - (Supporting Information) for the correlations for σ(C-H) tion for the population of C R bonds is nonlinear. The orbitals). degree of nonlinearity and the extent of electron transfer from the C-R bonds to the cationic center increase lation of C2-Hax bond in equatorial cation (1.963-1.967e) noticeably for the more polarizable bonds involving and C2-C3 (1.974-1.982) in axial cation are almost heavier elements. negligible. Although these orbitals are vicinal to the The extent of charge transfer from the remote donor positive centers, they do not overlap with the vacant substituents R to the acceptor p-orbital can also be

FIGURE 11. Correlations of the population of donor (σ(C-C) and σ(C-R)) orbitals in the equatorial cyclohexyl cations with electronegativity of elements in periods [B3LYP/6-31G**(B3LYP/6-311++G**) level]. See the Supporting Information (Figure S4) for the combined correlation.

9018 J. Org. Chem., Vol. 69, No. 26, 2004 Effect of Double-Hyperconjugation on the Donor Ability of σ-Bonds

TABLE 2. Populations (in Electrons) of the σ(C-R), σ(C-C), Σ(C-H)ax, and σ*(C-C) NBOs in Equatorial and Axial Cyclohexyl Cations Computed at the B3LYP/6-31G** (B3LYP/6-311++G**) Level (See the Tables in the Supporting Information for Further Details)

a The average values for the population of σ*(C2-C3)/σ*(C5-C6) and σ(C3-Hax)/σ(C5-Hax) pairs of orbitals are given.

TABLE 3. Natural Charge (Electron) on C1 in Cyclohexyl Cations; Populations (Electron) of Acceptor n(C1) NBOs and of Donor σ(C-C) and σ(C-H)ax NBOs in the Equatorial and Axial Cations, Respectively (at the B3LYP/6-31G** (B3LYP/ 6-311++G**) Level)

a The average values for the population of σ(C2-C3)/σ(C5-C6) and σ(C3-Hax)/σ(C5-Hax) pairs of orbitals are given. estimated from the NBO population of formally vacant ceptors have the opposite effect. Again, higher polariz- p-orbital at the cationic center. Figure 12 shows contrast- ability of the C-R bonds of higher periods leads to a ing behavior of the respective equatorial and axial cations stronger hyperconjugative response to the presence of a which further illustrates the efficiency of double hyper- cationic center and deviations from the simple linear conjugation. In equatorial cations, electron donor δ-sub- correlations. stituents efficiently transfer electron density to the Despite the complexity of the above correlations, the electron deficient carbon. Not surprisingly, electron ac- differences in populations of both nC1 and σ(C-R) orbitals

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FIGURE 12. Contrasting correlations of the population of cationic p-orbital with electronegativity of δ-substituents in equatorial (left) and axial (right) cyclohexyl cations at the B3LYP/6-31G**(B3LYP/6-311++G**) level. See Figure S5 (Supporting Information) for the correlation of charge C1 with population of n(C1).

FIGURE 13. Correlations of changes of populations of σ(C-R) and nC1 orbitals between axial and equatorial cations with ∆SEeq-ax values [B3LYP/6-31G**(B3LYP/6-311++G**) level].

FIGURE 14. Correlations of populations of σ(C-C) and σ*(C-C) bridge orbitals with ∆SEeq-ax values at B3LYP/6-31G** (B3LYP/ 6-311++G**) level. between the axial and equatorial cations correlate very the two acceptors as indicated by increased population well with ∆SEeq-ax values (Figure 13) illustrating internal of σ(C-C) orbitals and decreased population of σ*(C-C) consistency of these parameters in description of the (Table 2, Figure 14). Thus, the C-C bond is not a same physical phenomenonsdouble hyperconjugation. spectator but a dynamic gating factor capable of fine- Based on these results, treatment of the bridge C-C tuning double hyperconjugationsshutting it off when a bond is a simple “transmitter” of the interaction between strong acceptor is present at the δ-position or opening it the cationic center, and the C-R bond can be used only up when a strong donor at this position is available. for the most general qualitative discussions. Although (b) Dissection of Hyperconjugative Interactions. the sum of σ(C-C) and σ*(C-C) populations remains The NBO analysis allows dissection of double hypercon- almost constant and only a little charge is transferred jugation into components and gives further insight into from the bridge C-C moiety to the cationic center, its nature, e.g., the active role of the bridge C-C orbital electron acceptors (e.g., F, O, etc.) increase localization in communication of the donor and acceptor moieties. In of the bridge C-C bonds preventing communication of a possible scenario, electron density from the σ(C-R) 9020 J. Org. Chem., Vol. 69, No. 26, 2004 Effect of Double-Hyperconjugation on the Donor Ability of σ-Bonds

TABLE 4. Second-Order Perturbation Energies (kcal mol-1) for the Major Interactions Involved in the Equatorial and Axial Cations of Various Cyclohexane Derivatives from NBO Computations at the B3LYP/6-31G** (B3LYP/6-311++G**) Level and the Average Energy Values of Any Pair of Interactions (See the Tables in the Supporting Information for Further Details)

FIGURE 15. Resonance contributions to double hyperconjugation.17 to the nature of δ-substituents and, thus, the σ bridge indeed plays an active role in positive charge delocalization. As expected, electropositive substituents increase energies of these hyperconjugative donations (Figure 17). These correlations are not perfectly linearsthe presence of the most electropositive substituents leads to a steeper increase in the hyperconjugative energies which parallels enhanced polarizability of these bonds.41-43 Although the numerical accuracy of perturbative NBO analysis decreases in highly delocalized structures, and these energies should be taken only as a qualitative guide in the

FIGURE 16. Overlap of donor and acceptor NBOs for the σ- (C-C) f n(C+) (a) and σ(C-H) f σ*(C-C) (b) interactions in (41) Again, comparison of these effects with the axial cations given the equatorial cyclohexyl cation. in Supporting Information provides a useful reference point. Clearly, sensitivity of σ(C-H) f n(C) interaction in the axial cations cations to the nature of R is noticeably lower. donor is transmitted to the highly polarized and electron (42) Interestingly, the σ(C-R) f σ*(C-C) and σ(C-C) f n(C) - interactions are cooperative26sthe energies for two interactions to- deficient bridge C C bond in the first step. This increase gether are larger than the sum of the individual energies obtained from in electron density makes the bridge orbital a better the NBO deletion procedure. An interesting question is whether this donor and allows it to transfer, in the second step, the cooperativity indicates that, in the case of strong σ donors, the strong through-bond interaction pattern gradually transforms into a 6e acquired electron density further to the vacant p-orbital σ-aromatic system. (Figure 16). In such a case, energies of respective (σ- (43) It is interesting that these donor/acceptor interactions are (C-R) f σ*(C-C) and σ(C-C) f n(C1) hyperconjuga- topologically similar to theorbital interactions of two σ radicals through σ* bridge orbitals which plays an important role in the chemistry of tive interactions should increase as R becomes a better 1,4-diradicals. Hoffmann, R.; Imamura, A.; Hehre, W. J. J. Am. Chem. donor. Soc. 1968, 90, 1499. Squires, R. R.; Cramer, C. J. J. Phys. Chem. A The NBO energies of σ(C-R) f σ*(C-C) and σ(C-C) 1998, 102, 9072. Hoffner, J.; Schottelius, J.; Feichtinger, D.; Chen, P. f + J. Am. Chem. Soc. 1998, 120, 376. Kraka, E.; Cremer, D. J. Am. Chem. n(C ) interactions in Tables 4 and 5 show that the Soc. 2000, 122, 8245. Alabugin, I. V.; Manoharan, M. J. Am. Chem. magnitudes of both of these interactions respond strongly Soc. 2003, 125, 4495.

J. Org. Chem, Vol. 69, No. 26, 2004 9021 Alabugin and Manoharan

TABLE 5. NBO Deletion Energies (kcal mol-1) for the Major Interactions Involved in the Equatorial and Axial Cyclohexyl Cations at the B3LYP/6-31G** Level (See the Supporting Information for Further Details)

FIGURE 17. Correlations of NBO deletion energies (B3LYP/6-31G**) corresponding to the pairs of σ(C-R) f σ*(C-C) interactions (a) and σ(C-C) f n(C1) interactions (b) with the electronegativity of the corresponding elements of substituent (see Figures S7 and S8 (Supporting Information) for more details). estimate of relative importance of σ(C-R) f σ*(C-C) and we have shown that even though one cannot expect σ(C-C) f n(C+) interactions, it is clear that the coopera- hyperconjugative donor ability to be the only determining tive effects of these interactions are sufficiently large to factor in these systems, structural, electronic, and energy overshadow the relatively small intrinsic differences in contributions from double hyperconjugation combine in the donating ability of C-C and C-H bonds. a highly consistent picture. On the General Order of Donor Ability of σ Since SEeq values are defined as the apparent stabiliz- Bonds. Although the main topic of this paper involves ing effect of the substituent relative to unsubstituted energetic, structural, and electronic consequences of cyclohexyl cation, they can be taken to represent “appar- double hyperconjugation, the results pose an intriguing ent” donor ability of substituent R as a whole. However, question. Can one take the relative order of substituents SEeq include contributions from many effects in addition effects on the relative stabilities of “equatorial” cations to pure σ donation and, thus, should not be confused with as an experimentally verifiable general scale of donor the donor ability of the respective σ(C-R) bond. These - ability of σ C R bonds? An advantage in developing such values change as follows: Al > Ga . Ge g Si > As g B a scale based on these systems would be that the donor > C g H > P > N > Se > O g S > Br > Cl g F. The and acceptor sites are not directly connected.44 Ideally, ∆SEeq-ax values (Table 1) provided by eq 3 give an when local steric and electrostatic effects are minimized, estimate of σ donor ability which follows the order of the hyperconjugative contributions to the observable (Al,Ga) . Ge > As g Si > P > B > Se> H > C > S > experimental values should become more obvious. Indeed, Br > N > Cl > O > F(g means that difference is less than 0.5 kcal/mol, . stands for the difference more than (44) Interestingly, group-transfer energies are dominated by the electronegativity effects in the case of directly connected atoms, e.g.: 3 kcal/mol). Although this scale does not isolate hyper- Wiberg, K. B. Acc. Chem. Res. 1999, 32, 922. conjugation completely from other components, these 9022 J. Org. Chem., Vol. 69, No. 26, 2004 Effect of Double-Hyperconjugation on the Donor Ability of σ-Bonds stabilization energies are practically useful, chemically sites are not directly connected. Other points one has to meaningful and can be verified experimentally as out- consider in developing a general scale of donor ability of lined recently by Rauk and co-workers.15 σ bonds are the greater sensitivity of C-X bonds toward Not surprisingly, the two above scales of donor ability heavier elements to increased electronic demand (in- are different. Interestingly, the relative positions of creased polarizability) and the active role of the σ bridge connecting donor and acceptor orbitals. In light of these carbon and hydrogen switch. According to SEeq values findings, it would be very interesting to reexamine some (“apparent” donor ability of substituent R) the CH3 group is a stronger donor than the H substituent, a trend which of the literature controversies regarding the relative donor abilities of σ bonds and to determine whether some is reversed according to ∆SE - values (“apparent” eq ax of them were fueled by similar differences in the defini- hyperconjugative donor ability of σ(C-R) bond). In ad- tions.45 dition, similar switches are observed for a number of other pairs including potentially important combinations of other orbitals of similar donor ability (Cl/O, Br/O, S/O, Conclusions B/P, C/P, N/Se etc.). To analyze to what extent the Importantly, the order of donor ability of σ bonds in ∆SEeq-ax scale is influenced by a nonperfect compensation organic molecules is not “set in stone” because bonds in of the nonhyperconjugative effects, one can also consider carbon-based networks efficiently communicate with each relative trends from more rigorous quantum-mechanical other through double hyperconjugation and other “second estimate provided by NBO analysis. Values of σ(C-R) sphere” effects. Such interactions can efficiently change f σ*(C-C) energies (Table 5) which, in principle, should the intrinsic order of donor ability of σ bonds as il- be the most straightforward criterion of donor ability) lustrated by the order of apparent donor ability of C-H suggest that Al > Ga . Ge > Si > As . Se > P > B > and C-C bonds in δ-substituted cyclohexyl cations. Br > H > S . Cl > C > N > O > F. The “anomalous” The systematic differences between elements from positions of Br and Cl are not surprising because the different periods such as the higher polarizability of σ polarizable C-Br and C-Cl bonds are indeed moderately bonds with heavier elements is another reason one has strong donors. Unfortunately, σ(C-R) f σ*(C-C) ener- to be careful in developing a “truly general” trend in the gies are influenced not only by the donor ability of σ donor ability of σ bonds. Even when two C-X and C-Y bonds but also by the changing acceptor ability of σ*(C- σ bonds, with X and Y from different rows, display similar C) bonds in different cyclohexyl cations which is, in turn, donor ability in neutral molecules close to their energy modified by the difference in the acceptor properties of minimum conformation, these bonds will respond differ- the corresponding C-R antibonds (vide infra). Interest- ently to structural perturbation such as introduction of a cationic center. ingly, when σ(C-R) f σ*C-C) and σ(C-C) f n(C1) interactions (Table 5) are added to account for the second Finally, σ bridge connecting the donor and acceptor component in the double hyperconjugation array, the moieties shows remarkable behavior. Although the net amount of charge is transferred from the bridge C-C relative order approaches that given by the ∆SE - eq ax moiety to the cationic center remains essentially con- scale: Ga > Al > Ge > Si > As > P > B > H > C > Se stant, electron acceptors increase localization of the > S > N > Br > Cl > O > F. Populations of σ(C-R) bonds bridge C-C bonds preventing communication of the two (Table 2) in equatorial cyclohexyl cations give a similar acceptors. Thus, the C-C bond is not a spectator but a order: Al,Ga . Ge > As,Si >P > B,Se >H, S > C . Br > > > > dynamic gating factor capable of fine-tuning double Cl N O F. Note that in all of the above trends s - - hyperconjugation shutting it off when a strong acceptor the C H bond remains a stronger donor than the C C is present or opening it up when a strong donor is bond and that the donor abilities decrease when going available. from left to right in a period and from bottom to top in a group. However, differences arise when elements of Acknowledgment. We are grateful to the National different periods are compared. These differences suggest Science Foundation (CHE-0316598), MARTECH, and that one has to be careful in defining the criteria of donor the 3M Co. (Untenured Faculty Award to I.A.) for their ability. Since criteria that are based on the NBO dissec- partial support of our research at Florida State Uni- tion of the wave function are not directly measurable versity, to Professors Joe Lambert (Northwestern) and experimentally, the discussion of which of the above NBO Arvi Rauk (Calgary) for stimulating discussions, and to criteria is the best from the purist point of view goes Farhan Bou Hamdan for carrying out initial computa- beyond the scope of this paper. On the other hand, even tions on this project. though the ∆SEeq-ax criterion is not perfect, the ∆SEeq-ax values can be determined experimentally. Moreover, they Supporting Information Available: Correlations of substituent stabilization energies of the “equatorial” and “axial” are based on physically and chemically meaningful cyclohexyl cations with electronegativity in different periods. phenomena and provide a useful estimate of the relative Correlations of the populations of donor and acceptor orbitals trends in donor ability of σ bonds. in cyclohexanes and cyclohexyl cations with electronegativity. Finally, we hope that the relative orders of the donor Correlations of NBO deletion energies of individual and abilities reported above will be useful for qualitative reasoning but we would like to caution against their (45) Obviously, the differences in the donor abilities of a C-X σ donor bond depend on the nature of the acceptor, topology of interac- noncritical applications. One of important conclusions tion, contribution of electrostatic and steric effects and substitution from this study is that the communication of σ bonds on the X atom. We expect that such effects may (and most likely will) change the apparent donor ability of σ bonds in stereoelectronic effects throughout the molecule has a large effect on the relative and require computational reexamination of such effects every time a donor abilities of σ bonds even when donor and acceptor new system is subject to investigation.

J. Org. Chem, Vol. 69, No. 26, 2004 9023 Alabugin and Manoharan combined hyperconjugative interactions with enelectronega- equatorial cyclohexyl cations. Cartesian coordinates of all tivity. Correlation of the relative energies of equatorial and optimized geometries computed at both B3LYP/6-31G** and axial cations with the hyperconjugative energies. The second- B3LYP/6-311++G** levels. This material is available free of order perturbation as well as the NBO deletion energies of charge via the Internet at http://pubs.acs.org. individual hyperconjugative interactions and the sum of the major hyperconjugative interactions involved in axial and JO048287W

9024 J. Org. Chem., Vol. 69, No. 26, 2004